Here we have two logical statements:
- [tex]\( p \)[/tex] which is false.
- [tex]\( q \)[/tex] which is true.
We want to find the result of the logical expression [tex]\( p \)[/tex] or [tex]\( q \)[/tex].
A logical OR operation ([tex]\( \vee \)[/tex] or [tex]\(\mid\mid\)[/tex]) works as follows:
- If at least one of the operands is true, the OR expression evaluates to true.
- If both operands are false, the OR expression evaluates to false.
Given:
- [tex]\( p \)[/tex] is false.
- [tex]\( q \)[/tex] is true.
Let's apply these values to the OR operation:
- [tex]\( p \)[/tex] or [tex]\( q \)[/tex] is:
- Since [tex]\( q \)[/tex] is true (and OR requires only one operand to be true for the whole expression to be true),
Therefore, [tex]\( p \)[/tex] or [tex]\( q \)[/tex] is true.
